Question

A 70.0 kg70.0 kg ice hockey goalie, originally at rest, has a 0.170 kg0.170 kg hockey puck slapped at him at a velocity of 41.5 m/s.41.5 m/s. Suppose the goalie and the puck have an elastic collision, and the puck is reflected back in the direction from which it came. What would the final velocities of the goalie and the puck be in this case? Assume that the collision is completely elastic

Answer 1

In a perfectly elastic collision
Using momentum conservation
Pi = Pf
m1V1i + m2V2i = m1V1f + m2*V2f
given that m1 = 70.0 kg & m2 = 0.170 kg
V1i = 0 m/sec
V2i = 41.5 m/sec.
0 + 0.170*41.5 = 70.0*V1f + 0.170*V2f = 7.055
Now other condition of the elastic collisions is that
V1f - V2f = V2i - V1i
V1f - V2f = 41.5 - 0
V1f - V2f = 41.5
70.0*V1f + 0.170*V2f = 7.055
Now Solving both equation
Multiply equation 1 with 0.170 and Add both of them
70.17*V1f = (41.5*0.170 + 7.055)
V1f = (41.5*0.170 + 7.055)/70.17 = 0.2010 m/sec
V1f = 0.2010 m/sec
V2f = V1f -41.5
V2f = 0.2010 - 41.5 = -41.299 m/sec
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